Some of the distinctive symbols of the ancient Spartan warrior were his armor and weapons. His helmet had a distinctive plume, nose guard, and aggressively slanted cheek plates. He also used a large bronze shield and a spear, both of these items being integral to the hoplite style of fighting many Greek armies used in ancient times. If you prefer minimalist tattoos and symbols to full figures, you can get a tattoo of just the Spartan helmet, or the three items arrayed together.
One basic idea for a spartan tattoo is the simple image of a spartan warrior. As with other idealized warriors from ancient times, his musculature will probably be highly, if not overly, idealized and defined. He could be standing in one of many positions, from an erect position resembling a solider standing guard at a post, to a more forward and aggressive stance reminiscent of a fighting position. You can work with your tattoo artist to figure out a position that conveys the connotations you have in mind.
The Spartan's military tactics relied on fighting in the hoplite formation: soldiers would create formations several ranks deep, use their large shields to protect themselves and the soldier adjacent to them, and their spears allowed warriors to fight from the second rank. This made an intact hoplite formation a formidable force on the battlefield, but the individual soldiers were particularly vulnerable once the formation broke. Because this was the historical spartan fighting tactic, a full hoplite unit of spartan warriors is another idea if you want a Spartan-themed tattoo.
The Battle of Thermopylae, popularized by Frank Miller's quasi-fictional account of the battle in his movie "300," was one of Sparta's most famous battles. Taking place during one of the wars between the city states of Greece and the Persian empire, a large, multi-city state, the Greek army was holding back a much larger Persian force by using the terrain at Thermopylae to bottle neck the Persian army, preventing them from bringing their superior numbers to bear. However, a local villager showed the Persian army a way around the bottle neck. With the tactic compromised, the Spartan King Leonidas sent the bulk of the Greek soldiers away and remained with a small contingent of Spartan soldiers. While the King and his contingent perished, they bought the retreating Greek soldiers an extra three days to get away, and supplement Greek armies in the future. Spartan tattoos can invoke this legendary history by including the word "Thermopylae," in Latin or Greek characters, on pieces of Spartan battle gear.